Summation notation of 2+4+6+8+10

The graph of f(x) was vertically translated down by a value of k to get the function g(x) = 5x + k. What is the value of k? A -7

Nadya [2.5K]

Answer:

${\boxed{\text{A. }\math{k = -7}}$

Step-by-step explanation:

The general rule for vertical translation of a function ƒ(x) ⟶ ƒ(x) + k .

A positive value of k means that the graph is shifted up by k units.

The graph of ƒ(x) was shifted from (0, 1) to (0, -6).

$\text{The graph was shifted down by seven units, so }{\boxed{\mathbf{k = -7}}$

4 0

4 years ago

Read 2 more answers

HELPPPP 100 points if you help!!!!

nignag [31]

Answer:

Part A)

Chorus:

$c(t)=15(1.12)^t$

Band:

$b(t)=2t+30$

Part B)

After 9 years:

The chorus will have about 41 people.

And the band will have 48 people.

Part C)

About approximately 11 years.

Step-by-step explanation:

We are given that there are 15 people in the chorus. Each year, number of people in the chorus increases by 12%. So, the chorus increases exponentially.

There are 30 people in the band. Each year, 2 new people join the band. So, the band increases linearly.

Part A)

Since after each year, the number of people in the chorus increases by 12%, the new population will be 112% or 1.12 of the previous population.

So, using the standard form for exponential growth:

$c(t)=a(r)^t$

Where a is the initial population and r is the rate of change.

We will substitute 15 for a and 1.12 for r. Hence:

$c(t)=15(1.12)^t$

This represents the number of people in the chorus after t years.

We are given that 2 new people join the band each year. So, it increases linearly.

Since there are already 30 people in the band, our initial point or y-intercept is 30.

And since 2 new people join every year, our slope is 2. Then by the slope-intercept form:

$b(t)=mt+b$

And by substitution:

$b(t)=2t+30$

This represents the number of people in the band after t years.

Part B)

We want to find the number of people in the chorus and the band after 9 years.

Using the chorus function, we see that:

$c(9)=15(1.12)^9\approx41.59\approx41$

There will be approximately 41 people in the chorus after 9 years.

And using the band function, we see that:

$b(9)=2(9)+30=48$

There will be 48 people in the band after 9 years.

Part C)

We want to determine after approximately how many years will the number of people in the chorus and band be equivalent. Hence, we will set the two functions equal to each other and solve for t. So:

$15(1.12)^t=2t+30$

Unfortunately, it is impossible to solve for t using normal analytic methods. Hence, we can graph them. Recall that graphically, our equation is the same as saying at what point will our two functions intersect.

Referring to the graph below, we can see that the point of intersection is at approximately (10.95, 51.91).

Hence, after approximately 11 years, both the chorus and the band will have approximately 52 people.

5 0

3 years ago

PLZ HELP NEED ASAP, much appreciated

Margaret [11]

Answer:

Ok that's not it

x=-1 then y=4

x=0 then y= 6

x=1 then y = 8

x=2 then y= 10

x=3 then y= 12

Step-by-step explanation:

when y=2x+6

you have to plug what it says x is in each of the equations.

For the first one it says x=-1

you then plug that in and you get y=2(-1)+6

then you go through PEMDAS and first you get y=-2+6

-2+6 = 4

therefore y=4

and you just go through the rest wiht that

Step-by-step explanation:

6 0

2 years ago

Which set of ordered pairs could represent a function? (2, 3), (2, 2), (2, 4), (2, 9), (2, –2) (1, 5), (2, 6), (1, 6), (4, 5), (

Ratling [72]

Given:

The set of ordered pairs in the options:

(a) (2, 3), (2, 2), (2, 4), (2, 9), (2, –2)

(b) (1, 5), (2, 6), (1, 6), (4, 5), (1, 4)

(c) (1, 0), (2, 0), (1, 3), (4, 3), (5, 7)

(d) (5, 1), (7, 3), (9, 5), (11, 7), (13, 9)

To find:

The set of ordered pairs that could represent a function.

Solution:

A set of ordered pairs represent a function, if there exist unique output (y-value) for each input (x-value).

In option (a) we have, five output values y=3,2,4,9,-2 for single input x=2. So, it is not a function.

In option (b) we have, three output values y=5,6,4 for single input x=1. So, it is not a function.

In option (c) we have, two output values y=0,3 for single input x=1. So, it is not a function.

In option (d), all inputs has unique output.

Therefore, the correct option is (d).

4 0

3 years ago

Read 2 more answers

Which of the following rotational symmetry is applied to the regular not

olya-2409 [2.1K]

9514 1404 393

Answer:

yes
yes

Step-by-step explanation:

A regular nonagon has vertices that are 360°/9 = 40° apart. Any rotation by a multiple of 40° will make the figure indistinguishable from the original.

Rotational symmetry of 40° applies.

Rotational symmetry of 200° applies.

6 0

3 years ago